Problem: Simplify the following expression: $k = \dfrac{1}{5r} - \dfrac{1}{2r}$
Answer: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $5r$ and $2r$ $\lcm(5r, 2r) = 10r$ $ k = \dfrac{2}{2} \cdot \dfrac{1}{5r} - \dfrac{5}{5} \cdot \dfrac{1}{2r} $ $k = \dfrac{2}{10r} - \dfrac{5}{10r}$ $k = \dfrac{2 -5}{10r}$ $k = \dfrac{-3}{10r}$